Manifolds modelled on the holomorphic 2-ball

• Grant number: 18/10522-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: October 01, 2018
• End date: March 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Henrique Grossi Ferreira
• Grantee: Hugo Cattarucci Botós
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

A central question in Riemannian Geometry is the following: when does a given manifold admit a certain geometric structure? We are particularly interested in the case of a disc bundle over a closed orientable surface equipped with complex hyperbolic structure. Our main goal is to describe a certain deformation space of complex hyperbolic structures on disc bundles over surfaces. It time allows, we also expect to search for new discrete invariants of discrete faithful representations of surface groups on the isometry group of the complex hyperbolic plane. (AU)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

BOTOS, HUGO CATTARUCCI. Orbifolds and orbibundles in complex hyperbolic geometry. Topology and its Applications, v. 341, p. 25-pg., 2023-10-04. (18/10522-8)

BOTOS, HUGO CATTARUCCI. Geometry over algebras. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 94, p. 25-pg., 2024-03-28. (18/10522-8)

BOTOS, HUGO C.; GROSSI, CARLOS H.. Quotients of the Holomorphic 2-Ball and the Turnover. TRANSFORMATION GROUPS, v. N/A, p. 63-pg., 2025-07-01. (18/10522-8)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

BOTÓS, Hugo Cattarucci. Orbibundles, complex hyperbolic manifolds and geometry over algebras. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.